Explore topic-wise InterviewSolutions in Current Affairs.

The area (in sq. units) bounded by the curves $C_1:y=2x-x^2,x\in R$ and $C_2:y=\tan \left(\frac{\pi }{4}x\right),x\in [0,2)$ is equal to

The equation of the lines represented by $4x^2+24xy+11y^2=0$ is/are

Let $A=\{u,v,w,z\}$ and $B=\{3,5\}$, then the number of relations from $A$ to $B$ is

The number of solutions of the equation $(|\sin x|-1)(5|\sin x|-1)=0$ in $[0,2\pi ]$ is

Let $f\left(x\right)>0$ for all $x$ and $f^{\prime }\left(x\right)$ exists for all $x$. If $f$ is the inverse function of $h$ and $h^{\prime }\left(x\right)=\frac{1}{1+\log x}$. Then $f^{\prime }\left(x\right)$ will be

The circle passing through the points $(1,0),(2,-7)$ and $(8,1)$ also passes through

If $2x^2{y}^2+y^2-6x^2-12=0,$ then number of integral pairs $(x,y)$ satisfying is/are

The common tangent to the circles $x^2+y^2=4$ and $x^2+y^2+6x+8y-24=0$ intersects the coordinate axes at $A$ and $B$ respectively. If $OA$ and $OB$ are equal to half of the length of the major and minor axes of an ellipse respectively, where $O$ is the origin, then the eccentricity of the ellipse is

The value of $2({\cos }^{2}73°+{\cos }^{2}47°)-\cos 154°$ is

The distance of the point $(3,8,2)$ from the line $\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-2}{3}$ measured parallel to the plane $3x+2y-2z=0$ is -

Let $ABCD$ be a square. An arc of a circle with $A$ as center and $AB$ as radius is drawn inside the square joining the points $B$ and $D$. Points $P$ on $AB$, $S$ on $AD$, $Q$ and $R$ on arc $BD$ are taken such that PQRS is a square. Further suppose that PQ and RS are parallel to AC. Then $\frac{\text{area}\left(PQRS\right)}{\text{area}\left(ABCD\right)}$is

Find the area bounded by the curve y = sin x between x = 0 and $x=2\pi$.

Find the area enclosed by the parabola $4y=3x^2$ and the line 2y = 3x+12. ?

If normal at $P(2,\frac{3\sqrt{3}}{2})$ meets the major axis of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ at $Q$ and $S,S^{\prime }$ are foci of given ellipse along positive and negative directions of axes, then the ratio $SQ:S^{\prime }Q$ is

The equation of the circle inscribed in the triangle formed by the straight line $4x+3y=6$ and both the coordinate axes is

$\int \frac{sinx+cosx}{\sqrt{1+sin2x}}dx=$

Let A = {p. q, r, s} and B = {1, 2, 3}. Which of the following relations from A to B is not a function?
(i) $R_1=\left\{\right(p,1),(q,2),(r,1),(s,2\left)\right\}$
(ii) $R_2=\left\{\right(p,1),(q,1),(r,1),(s,1\left)\right\}$
(iii) $R_3=\left\{\right(p,1),(q,2),(r,1),(s,2\left)\right\}$
(iv) $R_4=\left\{\right(p,2),(q,3),(r,2),(s,2\left)\right\}$

The equation(s) of tangents drawn from the point $(1,4)$ to the parabola $y^2=12x$ is/are

Let $f:X\to Y$ be an invertible function. Show that f has unique inverse

If $A=\left[\begin{array}{c}12\\ -13\end{array}\right]B=\left[\begin{array}{c}40\\ 15\end{array}\right]C=\left[\begin{array}{c}20\\ 1-2\end{array}\right]$,
a = 4, and b = - 2, then show that:

(i) A + (B + C) = (A + B) + C

(ii) A (BC) = (AB) C

(iii) (a + b)B = aB + bB

(iv) a (C - A) = aC - aA

(v) $(A^T{)}^T$ = A

(vi) $(bA{)}^T$ = b $A^T$

(vii) $(AB{)}^T=B^T{A}^T$

(viii) (A - B)C = AC - BC

(ix) $(A-B{)}^T=A^T-B^T$

${(1+\frac{x}{2}-\frac{2}{x})}^4,x\ne 0$

The determinant of the matrix$\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ is___

Prove that 33! Is divisible by $2^{15}$ what is the largest integer n such that 33! Is divisible by $2^n.$

If $\omega$ is a complex cube root of unity, then the equation whose roots are $2\omega$ and $2{\omega }^2$ is

If $2x^2+2y^2-12x+8y+k=0$ is a point circle, then the value of $k$ is

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

If the equation $(a-2)(x-[x]{)}^2+2(x-\left[x\right])+a^2=0,a\in R$ has no integral solution and has exactly one solution in $[2,3)$, then $a$ lies in the interval
(where $\left[x\right]$ denotes the greatest integer function)

In $△$ ABC, if (a+b+c)(a-b+c)=3ac, then
[AMU 1996]

The kindergarten teacher has $25$ kids in her class. She takes $5$ of them at a time, to zoological garden as often as she can, without taking the same $5$ kids more than once. Then the number of visits, the teacher makes to the garden exceeds that of a kid by

Please define me the power of set.

If 1,m and k are the roots of the cubic polynomial whose sum is 5 and sum of product of roots taken two at a time is 8, then value of (m-k) is,

Equation of the line of shortest distance between the lines $\frac{x}{2}=\frac{y}{-3}=\frac{z}{1}$ and $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$ is

If the line $\frac{x}{a}+\frac{y}{b}=\sqrt{2}$ touches the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ then the eccentric angle of point of contact is

What is difference between problems of conditional probability and bayes' theorem?

Domain of $\sqrt{(x^2+7x+10)\left(\ln \right(x+3){)}^2}$ is

If the equation $tan\theta +tan2\theta +tan\theta tan2\theta =1then\theta$ is equal to

so the least integral value of n is

The point of intersection of the lines $\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}and\frac{x-2}{1}=\frac{y-4}{3}=\frac{z-6}{5}$ is

The locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ is

A(1,1) and B(2,-3) are two points and D is a point on AB produced such that AD=3AB.Find the co-ordinates of D.

${lim}_{x\to \frac{\pi }{2}}\frac{1-sinx}{co{s}^{2}x}$

Using elementary row operations (transformations), find the inverse of $\left(\begin{array}{ccc}0& 1& 2\\ 1& 2& 3\\ 3& 1& 0\end{array}\right)$ OR If A = $\left[\begin{array}{ccc}0& 6& 7\\ -6& 0& 8\\ 7& -8& 0\end{array}\right]$, B = $\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 2\\ 1& 2& 0\end{array}\right]$, C= $\left[\begin{array}{c}2\\ -2\\ 3\end{array}\right]$, then calculate AC, BC and (A+B) C.

Also verify that (A+B)C = AC+BC.

A G.P. has even number of terms . If the sum of all the terms is $5$ times the sum of the terms occupying the odd places, then the common ratio of the G.P. is